Dice in various forms are utilized in a multitude of games. For example, in many casino wagering games it is commonplace to utilized dice to determine the player or playing position at the table where play commences (known as the "action player" or "action position"). Depending upon the specific gamer the action player is typically the first to receive cards, and is also the first to have his or her bet dispositioned. Three conventional dice are utilized to determine the action player. The dice are usually rolled by the player-bankers with a resulting numerical total ranging from 3 through 18 (sixteen numbers). Commencing with the player-bankers the numeric total of the three dice is then sequentially counted off clockwise, thereby establishing the action player. For example, in an eight handed game wherein player six was the player-banker, a dice roll of 13 would establish player 2 as the action player (6,7,8,1,2,3,4,5,6,7,8,1,2). This technique is somewhat cryptic in that the action player is not directly defined, but rather cumbersome and time consuming counting is required. A second disadvantage of the three conventional dice method is that the probability of all players becoming the action player is not equal. There are 216 (6.times.6.times.6) possible combinations of three dice. In an eight handed game, the probabilities of each player becoming the action player are as follows:
Player 1 28/216=0.130 PA1 Player 2 28/216=0.130 PA1 Player 3 28/216=0.130 PA1 Player 4 28/216=0.130 PA1 Player 5 27/216=0.125 PA1 Player 6 25/216=0.116 PA1 Player 7 25/216=0.116 PA1 Player 8 27/216=0.125
While the variation among players is not extreme, it would nevertheless be preferable to utilize a system wherein the probabilities for each player are identical.
Another disadvantage of the three conventional dice method resides in the fact that the dice can never sum to one or two. Therefore, no matter where the count is initiated (e.g. the last winner of the previous hand), the first two sequential players can never become the action player on the first round of counting.